__maths__>__Mensuration : Length, Area, and Volume__>__Mensuration: Two Dimensional Shapes__### Area of Polygons

*In the topic "mensuration", the foundation focuses on learning • what is measurement standard? • Absolute and Derived Standards*

In this topic, finding area of polygons is reviewed quickly.

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Consider the polygon shown in the figure. Which of the following help to find the area of the polygon?

- area of a polygon cannot be calculated
- consider the polygon as combination of triangles and find the sum of the areas of triangles
- consider the polygon as combination of triangles and find the sum of the areas of triangles

The answer is "consider the polygon as combination of triangles"

Consider the polygon shown in the figure. Area of the polygon

`=` area of `/_\ABD + ` area of `/_\DBC` + area of `/_\ADE`.

The formula for area of triangle is used to find the area of the polygons.

**Area of a Polygon** : Consider a polygon to be combination of known geometrical forms, mostly triangles.

The geometrical forms and the formula for area are:

Area of a triangle `= 1/2 xx text( base ) xx text( height)`

Area of a trapezium `= 1/2 xx text( sum of bases ) xx text( height)`

Area of a parallelogram `= 1/2 xx text( base ) xx text( height)`

Area of a kite `= 1/2 xx text( major-diagonal ) xx text( d2)`

*Solved Exercise Problem: *

What is the area of a quadrilateral with all internal angles `90^@` and two sides `4cm` and `3`cm?

- two triangles with combined area `2 xx 1/2 xx 4 xx 3 = 12cm^2`
- area of the rectangle `4 xx 3 = 12 cm^2`
- both the above
- both the above

The answer is "both the above"

*slide-show version coming soon*